QREigenComponentExtractor.java
package org.drip.numerical.eigen;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>QREigenComponentExtractor</i> extracts the Eigenvalues and Eigenvectors using QR Decomposition.
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/eigen">QR PICE Eigen-Component Extraction Methodologies</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class QREigenComponentExtractor
implements org.drip.numerical.eigen.ComponentExtractor
{
private int _maxIterations = -1;
private double _tolerance = java.lang.Double.NaN;
/**
* QREigenComponentExtractor Constructor
*
* @param maxIterations Maximum Number of Iterations
* @param tolerance Tolerance
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public QREigenComponentExtractor (
final int maxIterations,
final double tolerance)
throws java.lang.Exception
{
if (0 >= (_maxIterations = maxIterations) ||
!org.drip.numerical.common.NumberUtil.IsValid (
_tolerance = tolerance
) || 0. == _tolerance
)
{
throw new java.lang.Exception ("QREigenComponentExtractor ctr: Invalid Inputs!");
}
}
/**
* Retrieve the Maximum Number of Iterations
*
* @return The Maximum Number of Iterations
*/
public int maxIterations()
{
return _maxIterations;
}
/**
* Retrieve the Tolerance Level
*
* @return The Tolerance Level
*/
public double tolerance()
{
return _tolerance;
}
@Override public org.drip.numerical.eigen.EigenOutput eigenize (
final double[][] a)
{
org.drip.numerical.linearalgebra.QR qr = org.drip.numerical.linearalgebra.Matrix.QRDecomposition (
a
);
if (null == qr)
{
return null;
}
double[][] q = qr.q();
double[][] qTranspose = org.drip.numerical.linearalgebra.Matrix.Transpose (
q
);
if (null == qTranspose)
{
return null;
}
int iterationIndex = 0;
int eigenComponentCount = a.length;
double[] eigenvalueArray = new double[eigenComponentCount];
double[][] b = new double[eigenComponentCount][eigenComponentCount];
double[][] v = new double[eigenComponentCount][eigenComponentCount];
if (0 == eigenComponentCount || null == qTranspose[0] || eigenComponentCount != qTranspose[0].length)
{
return null;
}
for (int rowIndex = 0;
rowIndex < eigenComponentCount;
++rowIndex)
{
for (int columnIndex = 0;
columnIndex < eigenComponentCount;
++columnIndex)
{
b[rowIndex][columnIndex] = q[rowIndex][columnIndex];
v[rowIndex][columnIndex] = a[rowIndex][columnIndex];
}
}
while (iterationIndex++ < _maxIterations &&
org.drip.numerical.linearalgebra.Matrix.NON_TRIANGULAR ==
org.drip.numerical.linearalgebra.Matrix.TriangularType (
v,
_tolerance
)
)
{
if (null == (qr = org.drip.numerical.linearalgebra.Matrix.QRDecomposition (
v = org.drip.numerical.linearalgebra.Matrix.Product (
qTranspose,
org.drip.numerical.linearalgebra.Matrix.Product (
v,
q
)
)
)))
{
return null;
}
qTranspose = org.drip.numerical.linearalgebra.Matrix.Transpose (
q = qr.q()
);
b = org.drip.numerical.linearalgebra.Matrix.Product (
b,
q
);
}
if (iterationIndex >= _maxIterations)
{
return null;
}
for (int rowIndex = 0;
rowIndex < eigenComponentCount;
++rowIndex)
{
eigenvalueArray[rowIndex] = v[rowIndex][rowIndex];
}
try
{
return new org.drip.numerical.eigen.EigenOutput (
org.drip.numerical.linearalgebra.Matrix.Transpose (
b
),
eigenvalueArray
);
} catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Ordered List of Eigenvalues for the specified Eigen-output
*
* @param eigenOutput The Eigen Output
*
* @return The Order List
*/
public java.util.List<java.lang.Integer> eigenComponentOrderList (
final org.drip.numerical.eigen.EigenOutput eigenOutput)
{
if (null == eigenOutput)
{
return null;
}
double[] eigenvalueArray = eigenOutput.eigenValueArray();
int eigenComponentCount = eigenvalueArray.length;
java.util.List<java.lang.Double> eigenValueList = new java.util.ArrayList<java.lang.Double>();
java.util.List<java.lang.Integer> eigenValueOrder = new java.util.ArrayList<java.lang.Integer>();
for (int eigenComponentIndex = 0;
eigenComponentIndex < eigenComponentCount;
++eigenComponentIndex)
{
int eigenValueOrderSize = eigenValueOrder.size();
if (0 == eigenValueOrderSize)
{
eigenValueOrder.add (
eigenComponentIndex
);
eigenValueList.add (
eigenvalueArray[eigenComponentIndex]
);
}
else
{
int insertionIndex = 0;
for (int eigenValueOrderIndex = 0;
eigenValueOrderIndex < eigenValueOrderSize;
++eigenValueOrderIndex)
{
if (eigenvalueArray[eigenComponentIndex] <= eigenValueList.get (
eigenValueOrderIndex
))
{
insertionIndex = eigenValueOrderIndex;
break;
}
}
eigenValueOrder.add (
insertionIndex,
eigenComponentIndex
);
eigenValueList.add (
insertionIndex,
eigenvalueArray[eigenComponentIndex]
);
}
}
return eigenValueOrder;
}
/**
* Generate the Ordered List of Eigen Components arranged by Ascending Eigenvalue
*
* @param a Input Matrix
*
* @return The Ordered List of Eigen Components arranged by Ascending Eigenvalue
*/
public org.drip.numerical.eigen.EigenComponent[] orderedEigenComponentArray (
final double[][] a)
{
org.drip.numerical.eigen.EigenOutput eigenOutput = eigenize (
a
);
java.util.List<java.lang.Integer> eigenComponentOrderList = eigenComponentOrderList (
eigenOutput
);
if (null == eigenComponentOrderList)
{
return null;
}
double[] eigenValueArray = eigenOutput.eigenValueArray();
double[][] eigenVectorArray = eigenOutput.eigenVectorArray();
int eigenComponentCount = eigenComponentOrderList.size();
org.drip.numerical.eigen.EigenComponent[] eigenComponentArray =
new org.drip.numerical.eigen.EigenComponent[eigenComponentCount];
for (int eigenComponentIndex = 0;
eigenComponentIndex < eigenComponentCount;
++eigenComponentIndex)
{
int eigenComponentOrder = eigenComponentOrderList.get (
eigenComponentIndex
);
try
{
eigenComponentArray[eigenComponentIndex] = new org.drip.numerical.eigen.EigenComponent (
eigenVectorArray[eigenComponentOrder],
eigenValueArray[eigenComponentOrder]
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
return eigenComponentArray;
}
@Override public org.drip.numerical.eigen.EigenComponent principalComponent (
final double[][] a)
{
org.drip.numerical.eigen.EigenComponent[] eigenComponentArray = orderedEigenComponentArray (
a
);
return null == eigenComponentArray ? null : eigenComponentArray[0];
}
/**
* Generate the UD Form of the Input Matrix
*
* @param a The Input Matrix
*
* @return The UD Form
*/
public org.drip.numerical.linearalgebra.UD udForm (
final double[][] a)
{
org.drip.numerical.eigen.EigenComponent[] eigenComponentArray = orderedEigenComponentArray (
a
);
if (null == eigenComponentArray)
{
return null;
}
int eigenComponentCount = eigenComponentArray.length;
double[][] d = new double[eigenComponentCount][eigenComponentCount];
double[][] u = new double[eigenComponentCount][];
for (int eigenComponentIndexI = 0;
eigenComponentIndexI < eigenComponentCount;
++eigenComponentIndexI)
{
u[eigenComponentIndexI] = eigenComponentArray[eigenComponentIndexI].eigenVector();
for (int eigenComponentIndexJ = 0;
eigenComponentIndexJ < eigenComponentCount;
++eigenComponentIndexJ)
{
d[eigenComponentIndexI][eigenComponentIndexJ] = eigenComponentIndexI != eigenComponentIndexJ
? 0. : eigenComponentArray[eigenComponentIndexI].eigenValue();
}
}
try
{
return new org.drip.numerical.linearalgebra.UD (
u,
d
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}